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Science & Mathematics

The Museum's collections hold thousands of objects related to chemistry, biology, physics, astronomy, and other sciences. Instruments range from early American telescopes to lasers. Rare glassware and other artifacts from the laboratory of Joseph Priestley, the discoverer of oxygen, are among the scientific treasures here. A Gilbert chemistry set of about 1937 and other objects testify to the pleasures of amateur science. Artifacts also help illuminate the social and political history of biology and the roles of women and minorities in science.

The mathematics collection holds artifacts from slide rules and flash cards to code-breaking equipment. More than 1,000 models demonstrate some of the problems and principles of mathematics, and 80 abstract paintings by illustrator and cartoonist Crockett Johnson show his visual interpretations of mathematical theorems.

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The lithographic firm of Sarony, Major & Knapp (1857–1867) of New York printed this lithograph of “Cascades of the Columbia” originally drawn by John M. Stanley (1814–1872) of Detroit (1834–1840, 1864–1872) and Washington, D.C. (1850–1860). The illustration was printed as Plate XLV in the “General Report” of volume XII of Reports of Explorations and Surveys, to ascertain the most practicable and economical route for a railroad from the Mississippi River to the Pacific Ocean, “Narrative Final Report of Explorations for a Route for a Pacific Railroad, near the Forty–Seventh and Forty–Ninth Parallels of North Latitude, St. Paul to Puget Sound”. The volume was printed in 1860 by Thomas H. Ford in Washington, D.C.

By the 1920s, companies in the United States, Germany, and France manufactured inexpensive notched band adders. A firm in Marseille, France, under the direction of engineer E. Reybaud, sold this device from 1922 until at least 1930. This example was from the collection of L. Leland Locke.

The metal adder and stylus fit into a red paper container. The adder has nine columns of digits and a zeroing bar at the top. Instructions indicate that the device came in two models that sold for 25 and 40 francs. This was sufficiently inexpensive that every member of a commercial firm could have such an adder.

Adders like this one were designed to help consumers with addition, but did not actually add automatically. The surface of the metal instrument has seven slots that reveal part of seven flat notched metal bands below. To enter a digit, one pulls down a band with the metal stylus. The hooked shape of the slots exposed a notch in an adjacent band, making it possible to carry or to borrow digits. This adder also has a zeroing bar at the base. It fits into a dark brown paper case.

Instruments of this type appeared as early as the 1600s, and sold commercially from the 1890s into the 1970s. They sold in Germany from the invention of the “Trick” in 1911. Otto Meuter patented a variation on this device that sold as the Arithma from 1920. Meuter received a fixed fee for each Arithma produced. With inflation, this sum soon was minute.

Meuter decided to form another company with J. Bergmann and to market adders known as the Pro Calculo! and the Correntator. These sold widely in the 1920s. For example, the trade magazine Typewriter Topics reported that 15,000 ProCalculo! adders sold in 1926. In 1928, the product was renamed the Produx.

The orange, black, and tan paper box contains a black and gold-colored metal instrument, instructions on pink paper, and a metal stylus. The device has seven columns for addition.

The Baby Calculator was a handheld adder manufactured by the Calculator Machine Company of Chicago from at least 1925 into the 1940s. The Tavella Sales Company of New York City distributed this example. According to the box, it sold for $2.50 in the United States and $3.00 in Canada and other foreign countries. It has hooks at the top of each column for carrying in addition, but none at the bottom to assist in borrowing in subtraction.

This aluminum device consists of two discs sealed together at the rim, with a rotating disc in between. Various numbers are stamped around the rim of the rotating disc. Openings in the outer discs reveal three numbers on either side at one time. One side of the instrument has the numbers from 1 to 20 stamped clockwise around the scalloped rim of the movable disc. The other side of this disc has the numbers from 21 to 40, also stamped clockwise.

At the top of the instrument, three alternate numbers are visible (i.e., 1, 3, 5). Three alternate numbers also are visible on the reverse side (i.e., 35, 37, 39). The sum of two numbers on opposite sides of the disc is always 40 (i.e., 1 and 39). Part of the scalloped edge of the movable disc is exposed at the bottom.

Clay W. Prewett and the Prewett Addograf and System Company (also known as the Prewett System Company) of Los Angeles, California, sold this device. A 1940 brochure describing “The Prewett Addograf and System” indicated that it consisted of not only this instrument but a $10 brochure describing how it worked, a $5 brochure on modern short cuts in multiplication, division, interest, fractions, and mixed numbers; and a $5 multiplication chart. The entire system could be purchased for $15. It was not returnable.

The first American-made adder to enjoy modest commercial success was developed by Clarence E. Locke (1865-1945). A native of Edgerton, Wisconsin, he graduated from Cornell College in Mt. Vernon, Iowa, in 1892. Locke worked for a time as a civil engineer in Minnesota, and then joined his father operating a lumber yard in Kensett, Iowa.

This version of the device has a metal base with grooves for nine sliding metal rods that move crosswise. Each rod represents a digit of a number being added. Protruding knobs on the rods represent different numerals. The rods are held in place by bronze-colored metal covers that extend over the right and left thirds of the instrument. When the device is in zero position, all the rods are in their rightmost position.

Numbers are entered by sliding rods to the left, and the result appears in numbers immediately to the left of the cover on the right. The rods are color-coded to distinguish units of money. They lock when depressed, so that they will not slide if the instrument is tilted. The locking mechanism, the color-coded rods, and the oval shape of the knobs on the rods are all improvements featured in Locke’s second calculating machine patent, taken out in 1905. There is no carry mechanism. The base of is covered with green cloth.

The instrument is marked on the right cover: C. E. LOCKE (/) MFG. Co. It also is marked: KENSETT, IOWA. [/] U.S.A. It is marked on the left cover: THE (/) LOCKE (/) ADDER. It also is marked: PATENTED DEC. 24. 1901 (/) JAN. 3 1905. This example came to the Smithsonian from the collection of L. Leland Locke.

The instrument resembles MA.323619, but it has green rather than red cloth on the bottom and has no surrounding wooden box. Also compare to MA.321327.

The wooden ruler also serves as a stylus-operated non-printing adding machine. It has a plastic inset along the middle, with a perforated paper strip that moves below the plastic. The numbers from 1 to 45 are marked along one edge of the plastic and from 46 to 90 along the other. A small dial and a window are at one end. Instructions are given on a plastic insert on the reverse of the rule. The number in the window indicates units and tens, while those around the dial denote hundreds. Only one of the hundreds digits (3) is marked. There is no stylus. One edge of the ruler is beveled and has a brass insert. This edge is marked off with a scale 15 inches long, divided to 1/16 inches.

The device is marked: PERFECTION (/) SELF-ADDING RULER (/) PAT. JAN. 8th 1895. No place of manufacture is indicated. The inventor, Robert E. McClelland, lived in Williamsville, Illinois. Later versions of the rule indicate that it was made in New York.

This metal model was constructed by Richard P. Baker. A mathematics professor at the University of Iowa, Baker believed that models were essential instruction in many parts of mathematics and physics. Over one hundred of his models are in the NMAH collections.

This painted wire structure is a model for Desargues' Theorem. A paper tag reads: No. 49a Desagues' Theorem by (/) projection (/) Triangles in different (/) planes. This version of the model is not listed in Baker's 1905 catalog, but is included in the 1931 catalog. The model sold for $2.50.

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections. Baker mentioned the model in a 1905 listing of one hundred models he had constructed as well as in a 1931 catalog.

A typed paper label on the top of the wooden base of this model reads: No. 72 (/) TWISTED CUBIC (/) (by cone and cylinder).

Like several other models Baker made, this shows ruled surfaces, also called scrolls. Such a surface is swept out by a moving line. The two ruled surfaces shown here are a cylinder, indicated with red threads, and a double cone, indicated in yellow. The points where the surfaces intersect are indicated by a wire. The curve of intersection is of degree three and is known as a twisted cubic.

The model sold for $4.00.

References:

R. P. Baker, A List of Mathematical Models, [1905], p. 13.

R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 72.

R. P. Baker Papers, University of Iowa, Iowa City, Iowa.

George Salmon, A Treatise on the Analytic Geometry of Three Dimensions, Dublin: Hodges, Foster, and Company, 1874, esp. pp. 303-313.

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections. Baker mentioned the model in a 1905 listing of one hundred models he had constructed as well as in a 1931 catalog.

A typed paper label on the top of the wooden base of this model reads: No. 74 (/) TWISTED CUBIC: 3 real (/) asymptotes.

Like several other models Baker made, this shows ruled surfaces, also called scrolls. Such a surface is swept out by a moving line. This model shows portions of three hyperbolic cylinders, one with yellow strings, one with blue strings, and one with red strings (a hyperbolic cylinder is a surface that joins two parallel hyperbolas, just as a regular cylinder joins two parallel circles. For a model, see 1982.0795.33). The hyperbolic cylinders in this model all make an acute angle with the base. Three pieces of wire indicate places where the three hyperbolic cylinders intersect. These are part of a curve of degree three known as a twisted cubic, in this case a twisted cubic with three real asymptotes.

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections. Baker mentioned the model in a 1905 listing of one hundred models he had constructed as well as in a 1931 catalog.

A typed paper label on the top of the wooden base of this model reads: No. 75 (/) CUBICAL HYPERBOLIC PARABOLA.

Like several other models Baker made, this shows ruled surfaces, also called scrolls. Such a surface is swept out by a moving line. This model shows portions of a parabolic cylinder (going crosswise) and a hyperbolic cylinder (with two opposite sections, extending vertically). One asymptotic plane of the hyperbolic cylinder is parallel to what Sommerville calls the axial plane of the parabolic cylinder. The cylinders intersect in two curves which are represented by wires in the model. These wires are part of a cubical hyperbolic parabola.

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections. Baker mentioned the model in a 1905 listing of one hundred models he had constructed as well as in a 1931 catalog.

A typed paper label on the top of the wooden base of this model reads: No. 76 (/) TWISTED CUBIC: CUBICAL (/) PARABOLA. A mark incised in the base at the front reads: 76 R.P.B.

Like several other models Baker made, this shows ruled surfaces, also called scrolls. Such a surface is swept out by a moving line. This model shows portions of a parabolic cylinder (going crosswise with blue strings) and a hyperbolic paraboloid (in red strings). A metal wire along the points of intersection indicates the cubical parabola.

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.

The typed part of a paper label on the bottom of the wooden base of this model reads: No. 78 (/) CUBIC CONE WITH NODAL LINE. Model 78 appears on page 7 of Baker’s 1931 catalog of models as “With nodal line” under the heading Cubic Cones . It also appears in his 1905 catalog of one hundred models.

Baker’s string models always represent a special type of geometric surface called a ruled surface. A ruled surface, sometimes called a scroll, is one that is swept out by a moving line. This model shows two ruled surfaces. One of these surfaces is swept out by any of the threads connecting the curved vertical wooden sides of the model. The other ruled surface is swept out by any of the threads joining the curved horizontal piece of wood on the top of the model to the wooden base of the model. All the threads of this model pass through a point in the center of the model, which is the intersection of two special lines, one for each ruled surface.

The special line for the surface joining the vertical sides is the line connecting the inflection points of the cubic curves, i.e. the points where the curve changes from concave upward to concave downward (for the curve y=x3, it would be at the origin). This line is horizontal and passes over the center of the base.

The special line for the other curve is the vertical line going through the center of the base. It is formed by connecting the point where the upper curve crosses itself with the center of the base, which is also the point where the curve on the base crosses itself. A point of curve where the curve crosses itself is called a node, so all points of this vertical line are nodes and this is the nodal line of the surface.

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.

The typed part of a paper label on the top edge of the wooden frame of this model reads: No. 81 (/) CUBIC CONE: (/) CUSPIDAL EDGE.

Baker’s string models represent a special type of geometric surface called a ruled surface. A ruled surface, sometimes called a scroll, is one that is swept out by a moving line. This model shows the ruled surface swept out by the yellow threads connecting the sides, base, and top of the model.

A version of the model sold for $4.50, but it may have been considerably smaller.

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.

The typed part of a paper label on the bottom of the wooden base of this model reads: No. 82 (/) cubic cone: SINGLE SHEET (/) only.

Baker’s string models represent a special type of geometric surface called a ruled surface. A ruled surface, sometimes called a scroll, is one that is swept out by a moving line. This model shows the ruled surface swept out by the yellow threads connecting the curved vertical wooden sides of the model and by the threads joining the curved horizontal piece of wood on the top of the model to the curved piece at the front. All the threads of this model pass through a point in the center of the model which intersects a wire rising from the base.

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections. Baker mentioned the model in a 1905 listing of one hundred models he had constructed as well as in a 1931 catalog.

A typed paper label on the top of the wooden base of this model reads: No. 83 (/) CYLINDROID.

Like several other models Baker made, this shows a ruled surface, also called a scroll. Such a surface is swept out by a moving line. This line is represented by the blue string in the model. The string rotates periodically about the vertical access, and at the same time moves uniformly up (or down) the vertical axis. The surface also is known as Plücker’s conoid after the German mathematician and physicist Julius Plücker.

This string model was constructed by Richard P. Baker, possibly before 1905, when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.

The typed part of a paper label on the wooden base of this model reads: No. 84 Quartic Scroll, (/) with two nodal straight (/) lines. Model 84 appears on page 8 of Baker’s 1931 catalog of models as “Quartic Scroll , with two nodal straight lines.” The equation of the model is listed as (x2/((z - 1) 2)) + (y2/((z + 1) 2)) = 1. It also appears in his 1905 catalog of one hundred models.

Baker’s string models always represent a special type of geometric surface called a ruled surface. A ruled surface, sometimes called a scroll, is one that is swept out by a moving line. This model is swept out by any of the yellow threads joining the elliptically shaped horizontal piece of wood on the top of the model to the wooden base of the model.

In addition to the yellow threads of the model, there are two horizontal red threads that run from the rods at near the edge of the base and are parallel to the lines connecting the midpoints of the opposite sides of the square of surface of the base. There is a segment of each of these red threads for which each point meets two different lines of the model and the points of these segments are called double points, or nodes, of the surface. Thus these line segments are the two nodal lines of the model. The horizontal plane z = 1 intersects the model at the upper horizontal thread, while the horizontal plane z = -1 intersects it at the lower horizontal thread. When z=1, the points of intersection are (0,y,1) for y between -2 and 2. When z=-1, the points of intersection are (x,0,-1) for x between -2 and 2. Thus the nodal lines are the line segments connecting (0,-2,1) to (0,2,1) and (-2,0,-1) to (2,0,-1).

When z = 0 the equation of the surface becomes x2 + y2 = 1, so the horizontal plane z = 0 intersects the model at the unit circle with center at the origin. For any other value of z, the equation of the surface is of the form (x2/a2) + (y2/b2) = 1, where a does not equal b. This is the standard form for the equation of an ellipse.

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.

The typed part of a paper label on the bottom of the wooden base of this model reads: No. 85 (/) SCROLL OF ORDER 8 (/) CONES WITH COMMON VERTEX.

Baker’s string models represent a special type of geometric surface called a ruled surface. A ruled surface, sometimes called a scroll, is one that is swept out by a moving line. This model shows the ruled surfaces generated by the double tangents of two spheres through a line. The two spheres are white balls with diameters of three inches and 1 ½ inches (7.6 cm. and 3.8 cm.). The tangent lines are in blue thread – each thread is tangent to both spheres and passes through the line shown in yellow thread. According to Baker’s label and catalogs, the surface is of degree eight.

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.

The typed part of a paper label on the top of the wooden base of this model reads: No. 89 (/) Diff. Geometry of a helix. The model illustrates several terms used to describe curves in three-dimensional space, using as an example the spiral curve on a cylinder known as a helix. In the model, the cylinder is represented by blue threads and the helix by a wire that twists along it. The point of interest, hereafter called P, is at the center, atop a wire extending perpendicularly from the base (the normal to the helix at the point). Shown with red threads is the osculating (kissing) plane to the helix at P. The red thread that passes through P represents the tangent line at P. The wire circular arc passing through P in the osculating plane represents part of what is called the osculating circle. The smaller circles joined by wires that pass through P form what is called the osculating cone.

Shown with yellow threads is a plane perpendicular to the osculating plane known as the normal plane. The thread on this plane that passes through P is called the binormal to the curve at P.

This is a model of lines of curvature on an ellipsoid. The rectangular wooden base supports a plaster half-ellipsoid with grid of ellipses drawn on it. A tag on the model reads: No. 90 (/) LINES OF CURVATURE ON (/) ELLIPSOID.

References:

R. P. Baker, A List of Mathematical Models, [1905], p. 16. A copy of this document is in the Baker Papers at the University of Iowa Archives.